Unlike discontinuous Galerkin methods, this construction only holds for particular element-wise polynomial spaces and element topologies. First, it is not straightforward to implement such continuity in aggregated meshes. Second, it can destroy the approximation properties of \(V_h^{\textrm {ag}}\) . Let us take a look at an ill-posed degree of freedom on the interface between two aggregates (purple nodes in Figure REF ). In a straightforward extension of the constraints in (REF ), such a degree of freedom would be constrained by the multiple aggregates that contain it.
This, together with the enforcement of \({C}^0\) -continuity, would couple the degrees of freedom between separate aggregates, and thereby could ruin approximation properties. In extreme cases, it can lead to over-constrained systems. This locking phenomenon has been analyzed in detail in [1]}.
